Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-4x+6y &= -2 \\ -6x-2y &= -4\end{align*}$
Explanation: Begin by moving the $x$ -term in the second equation to the right side of the equation. $-2y = 6x-4$ Divide both sides by $-2$ to isolate $y$ $y = {-3x + 2}$ Substitute this expression for $y$ in the first equation. $-4x+6({-3x + 2}) = -2$ $-4x - 18x + 12 = -2$ Simplify by combining terms, then solve for $x$ $-22x + 12 = -2$ $-22x = -14$ $x = \dfrac{7}{11}$ Substitute $\dfrac{7}{11}$ for $x$ back into the top equation. $-4( \dfrac{7}{11})+6y = -2$ $-\dfrac{28}{11}+6y = -2$ $6y = \dfrac{6}{11}$ $y = \dfrac{1}{11}$ The solution is $\enspace x = \dfrac{7}{11}, \enspace y = \dfrac{1}{11}$.